Question: Ben is 40 years older than Omar. Eleven years ago, Ben was 5 times as old as Omar. How old is Omar now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Omar. Let Ben's current age be $b$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $b = o + 40$ Eleven years ago, Ben was $b - 11$ years old, and Omar was $o - 11$ years old. The information in the second sentence can be expressed in the following equation: $b - 11 = 5(o - 11)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $o$ , it might be easiest to use our first equation for $b$ and substitute it into our second equation. Our first equation is: $b = o + 40$ . Substituting this into our second equation, we get the equation: $(o + 40)$ $-$ $11 = 5(o - 11)$ which combines the information about $o$ from both of our original equations. Simplifying both sides of this equation, we get: $o + 29 = 5 o - 55$ Solving for $o$ , we get: $4 o = 84$ $o = 21$.